`∀[c,t,t':ℤ].  uiff((c + t) ≤ t';c ≤ 0) supposing t = t' ∈ ℤ`

Proof

Definitions occuring in Statement :  uiff: `uiff(P;Q)` uimplies: `b supposing a` uall: `∀[x:A]. B[x]` le: `A ≤ B` add: `n + m` natural_number: `\$n` int: `ℤ` equal: `s = t ∈ T`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` uimplies: `b supposing a` prop: `ℙ` uiff: `uiff(P;Q)` and: `P ∧ Q` le: `A ≤ B` not: `¬A` implies: `P `` Q` false: `False`
Rules used in proof :  cut lemma_by_obid sqequalHypSubstitution sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isectElimination thin hypothesisEquality natural_numberEquality independent_isectElimination hypothesis addEquality intEquality because_Cache isect_memberFormation introduction sqequalRule productElimination independent_pairEquality isect_memberEquality lambdaEquality dependent_functionElimination axiomEquality equalityTransitivity equalitySymmetry voidElimination

Latex:
\mforall{}[c,t,t':\mBbbZ{}].    uiff((c  +  t)  \mleq{}  t';c  \mleq{}  0)  supposing  t  =  t'

Date html generated: 2016_05_13-PM-03_31_22
Last ObjectModification: 2015_12_26-AM-09_46_03

Theory : arithmetic

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